Poincar\'e polynomials of moduli spaces of stable maps into flag manifolds

TL;DR

This paper computes the Poincaré polynomial of moduli spaces of genus zero stable maps into flag manifolds for degrees one and two, using Bialynicki-Birula decomposition.

Contribution

It provides explicit calculations of Poincaré polynomials for these moduli spaces, advancing understanding of their topology.

Findings

Poincaré polynomial for degree one stable maps computed

Poincaré polynomial for degree two stable maps computed

Utilizes Bialynicki-Birula decomposition method

Abstract

By using Oprea's Bialynicki-Birula decomposition for the stack of genus zero stable maps to flag manifolds. We calculate the Poincar\'e polynomial of the moduli space in degree one and degree two.